What open source GIS application, or plugin for same, or separate utility (GUI preferred but command line OK) has as part of its functionality the ability to take any angle (and a center of rotation) and any CRS as an input, and output a custom CRS that creates the same maps only rotated by the angle? (I have found similar questions here and elsewhere but the answers involved ESRI software and/or were limited to UTM.)

In my specific application I am hoping to create for a QGIS project a custom CRS that produces rotated 67.5 degrees clockwise versions of maps produced with EPSG 102009 (or 102003, both conic). (If you want to know why see Projections for solar eclipse umbral paths)

(Rotating the canvas would be an alternative approach but there is a bug that throws the labels for the layers way off.)